Math Problem Statement

Explain how to plot a point in the rectangular coordinate system.

Solution

Let's complete this guide to plotting points in the rectangular coordinate system.

Explanation:

To plot a point (a,b)(a, b) in the rectangular coordinate system:

  1. If aa is positive, move a|a| units to the right along the x-axis from zero.
  2. If aa is negative, move a|a| units to the left along the x-axis from zero.
  3. Then, if bb is positive, move b|b| units upward parallel to the y-axis.
  4. If bb is negative, move b|b| units downward parallel to the y-axis.

Filled-In Example

For the example in the image, a specific point like (3,5)(3, 5) could be illustrated by:

  • Moving 3 units to the right along the x-axis.
  • Then moving 5 units upward along the y-axis.

Let me know if you want a different example or more explanation on this! Here are a few related questions for further exploration:

  1. What happens when both coordinates aa and bb are negative?
  2. How would you plot a point with coordinates (0,b)(0, b) or (a,0)(a, 0)?
  3. How can plotting points help with graphing linear equations?
  4. How do positive and negative coordinates determine the quadrant of a point?
  5. How would you explain plotting to someone new to the concept?

Tip: Always remember that the x-coordinate determines horizontal movement, while the y-coordinate determines vertical movement!

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Math Problem Analysis

Mathematical Concepts

Coordinate System
Plotting Points
Positive and Negative Coordinates

Formulas

Movement along x-axis and y-axis based on the coordinates (a, b)

Theorems

Cartesian Coordinate System

Suitable Grade Level

Grades 6-8